Finite Group Databasebeta

← Prev (#72183292) Next (#72183294) →

C₂³×C₃×C₈×C₁₉ #72183293

order	3648
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1548288
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₃×C₈×C₁₉
multiplicative	(ℤ/10968)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₁₆×C₁₉, C₂²×C₃×C₄×C₈×C₁₉, C₂⁴×C₃×C₈×C₁₉, …
maximal normal subgroup of	C₂³×C₃×C₁₆×C₁₉, C₂²×C₃×C₄×C₈×C₁₉, C₂⁴×C₃×C₈×C₁₉, …
maximal quotient of	C₂³×C₃×C₁₆×C₁₉, C₂²×C₃×C₄×C₈×C₁₉, C₂⁴×C₃×C₈×C₁₉, …
automorphism group of	C₃×C₈×C₄₅₇
outer automorphism group of	C₃×C₈×C₄₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.